Dynamical quantum phase transitions (DQPTs) have been studied in the extended $XY$ model under both noiseless and noisy linear driven staggered field cases. In the time-independent staggered field case, the model exhibits a single critical point where the transition occurs from the spin-liquid phase to the antiferromagnetic phase. In the noiseless ramp case, unlike the transverse field $XY$ model where DQPT always occurs for a quench crossing the single critical point, there is a critical sweep velocity above which the kinks corresponding to a DQPT are completely removed. Furthermore, in this case there are only two critical modes whose excitation probability is one-half. In the presence of a Gaussian white noise, we find that this critical sweep velocity decreases by increasing the noise strength, and scales linearly with the square of the noise intensity. A surprising result occurs when the noise intensity and sweep velocity are about the same order of magnitude: The number of critical modes is significantly increased, signaling a region with multiple critical modes. Furthermore, our findings indicate that the scaling of the dynamical free energy near the DQPT time is the same for both noiseless and noisy ramp quenches.

In this work, we propose a path-integral-inspired formalism for computing the quantum thermal expectation values of spin systems subject to magnetic fields that can be time dependent and can accommodate the presence of Heisenberg exchange interactions between the spins. This is done by deriving an effective magnetic field from the quantum partition function of the system to use in classical atomistic spin dynamics simulations and generalizes the formalism presented in our previous work [Phys. Rev. Res. 5, 043075 (2023)]. In special cases where the effective field can be computed exactly, we compare our results with exact/numerical diagonalization methods for both ferromagnetic and antiferromagnetic coupling. We show that our method works well across a large temperature range and can reproduce quantum expectation values for antiferromagnetic coupling, which is usually not possible with classical models.

Van der Waals layered ferromagnetic compounds with high two-dimensional electronic conductivity hold a strong potential for quantum computing, future unconventional superconductors, catalysts, batteries, and fuel cells. We suggest a minimal theoretical model to understand the magnetic properties of the metal-organic framework ${\mathrm{CrCl}}_2{\left(\mathrm{pyz}\right)}_2$ (pyz = pyrazine). Using a Hubbard model we show that the ground state is dominated by a specific configuration of delocalized electrons on the pyz sites with a ferrimagnetic coupling to the localized spins on the Cr sites. This model suggests a magnetic moment of $2{\mu }_B$ which is remarkably close to the experimental value of $1.8{\mu }_B$ [K. S. Pedersen et al., Nat. Chem. 10, 1056 (2018)]. From Weiss mean-field theory we predict a weak ferromagnetic Cr-Cr coupling of $\approx 0.9$ meV. This is consolidated by second-order perturbation theory of the Ruderman-Kittel-Kasuya-Yosida interaction yielding a Cr-Cr coupling of $\approx 5$ meV. Understanding the interactions in these types of compounds can facilitate designs of metal-organic compounds with tailored magnetic properties.

A variety of exotic spin-orbital entangled magnetic ground states is expected in $4d$ transition-metal oxides (TMOs) featuring an ideal octahedral environment and active $t_{2\mathrm{g}}$ orbitals, due to the comparable strength of spin-orbit coupling (SOC), superexchange interaction, and Hund's coupling ($J_{\mathrm{H}}$). However, for the TMOs with a $d^3$ electronic configuration, orbital degrees of freedom are supposed to be quenched and SOC is generally expected to play no role in determining the magnetic ground state. The present study, through comprehensive investigations of the structural and physical properties (using neutron diffraction, dc as well as ac magnetization techniques, electron-spin-resonance study, and specific-heat analysis), shows a canted antiferromagnetic ground state for $\mathrm{C}{\mathrm{a}}_3\mathrm{LiRu}{\mathrm{O}}_6$, having $\mathrm{R}{\mathrm{u}}^{5+}$ with $4d^3$ electronic configuration in an octahedral crystal field. In the magnetic ground state, the moments are predominantly aligned along the crystallographic $a$ axis. The dc magnetization study shows strong anisotropy and short-range correlations (SROs) persisting above the transition temperature. The SRO above the transition temperature is also confirmed from the specific-heat study. Our ab initio calculations corroborate these experimental observations by demonstrating the critical roles of SOC and strong hybridization between the Ru $d$ and O $p$ states in determining spin canting, and the 3D nature of magnetic exchange interactions.

This study investigates the giant magnetothermal resistance (GMTR) effect in a fully-bcc epitaxial $\mathrm{C}{\mathrm{o}}_{50}\mathrm{F}{\mathrm{e}}_{50}$/Cu multilayer through both experimental and theoretical approaches. The applied magnetic field results in a giant change of the cross-plane thermal conductivity (Δκ) of 37 $\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, which reaches 1.5 times larger than the previously reported value for a magnetic multilayer and records the highest value at room temperature among the other solid-state thermal switching materials working on different principles. We investigated the electron thermal conductivity for exploring the remarkable Δκ by the two-current-series-resistor model combined with the Wiedemann-Franz law. However, the result shows the electron contribution accounts for only 35% of the Δκ, indicating the presence of additional spin-dependent heat carriers. Further investigation of the lattice thermal conductivity, which is expected to be spin independent, using nonequilibrium molecular dynamics simulations suggests a striking contrast: the additional spin-dependent heat carrier contribution is significantly enhanced in the parallel magnetization configuration but nearly negligible in the antiparallel configuration. These findings provide a fundamental insight into the origin of large GMTR effect and highlight its potential of active thermal management technologies for future electronic devices.

A controlled and reversible transition between two topological states is a highly desirable feature in any spintronic system. Combining external magnetic field and hybrid magnetic anisotropy, we show in micromagnetism simulation a controlled transition between different $k\pi$-skyrmion states. With an oscillating magnetic field, we further achieve a transition from an initial state to the desired final state. We hence propose a skyrmion-based multibit storage that can be controlled by microwave.

The geometrically frustrated Kitaev magnets have been demonstrated to be fertile playgrounds that allow for the occurrence of exotic phenomena, including topological phases and the thermal Hall effect. Notwithstanding the established consensus that the field-polarized phase in the honeycomb-lattice Kitaev magnet hosts topological magnons exhibiting Chern numbers $C=\pm 1$, the nature of magnon excitations in Kitaev magnets on the star lattice, a triangle-decorated honeycomb lattice, has rarely been explored primarily due to its complicated geometry. To this end, we study the band topology of magnons on the star lattice in the presence of a strong out-of-plane magnetic field using linear spin-wave theory. By calculating the Chern numbers of magnon bands, we find that topological phase diagrams are predominantly composed of two distinct topological phases whose Chern numbers are different by a sign in inverse order. Remarkably, each phase is characterized by a high Chern number of either $+2$ or $-2$. In addition, several topological flat bands with large flatness are identified. The two phases are separated by a dozen narrow topological high-Chern-number segments, whose region shrinks as the magnetic field increases and vanishes eventually. We also find that the thermal Hall conductivity approaches zero at certain parameters, and it changes (keeps) its sign when crossing the topological phase-transition points (flat-band points).

We experimentally demonstrate coherent magnon-magnon coupling by thermal spin excitations in yttrium iron garnet/permalloy (YIG/Py) hybrid structures using microfocused Brillouin light scattering—an optical technique that enables the detection of zero-wave-vector and higher-order wave-vector spin waves in a broad frequency range. The thermally activated magnons in the bilayer lead to a hybrid excitation between magnon modes in the conductive Py layer with a wide wave-vector range and the first perpendicular standing magnon modes in the insulating YIG layer, facilitated by strong interfacial exchange coupling. To further investigate this coupling, we compare the thermal magnon spectra with the results obtained from electrical excitation and detection methods, which primarily detect the uniform Py mode. The realization of coherent coupling between incoherent (thermal) magnons is important for advancing energy-efficient magnonic devices, particularly in classical as well as quantum spin-wave computing technologies.

Photoemission electron microscopy (PEEM) has evolved into an indispensable tool for structural and magnetic characterization of surfaces at the nanometer scale. In strong contrast to synchrotron-radiation-based x-ray PEEM as a leading method for element-specific magnetic properties via magnetic circular dichroism (MCD), laboratory ultraviolet (UV) PEEM has seen limited application with much smaller dichroic effects for in-plane magnetization. Here, we introduce dark-field PEEM as an approach to enhance MCD contrast in threshold photoemission, enabling efficient MCD imaging with significantly enhanced contrast by an order of magnitude for Fe(001). This advancement paves the way for MCD imaging on femtosecond timescales using modern lasers. The experimental results will be quantitatively benchmarked against advanced relativistic photoemission calculations.

We propose a theoretical model to investigate the interplay between altermagnetism and $p$-wave superconductivity, with a particular focus on topological phase transitions in a two-dimensional $p$-wave superconductor, considering both chiral and helical phases. Our study reveals that the emergence of helical and chiral Majorana states can be tuned by the amplitude of a $d-\text{wave}$ altermagnetic order parameter, with the outcome depending on the nature of the superconducting state. In the helical superconductor, such an altermagnet can induce a topological phase transition into a gapless topological superconductor hosting Majorana flat edge modes. On the other hand, in the chiral superconductor, the topological transition takes place between a topologically nontrivial gapped phase and a gapless nodal-line superconductor, where the Bogoliubov quasiparticle bands intersect at an isolated line in momentum space. Remarkably, we show that when such an altermagnet is coupled to a mixed-pairing superconductor, with both chiral and helical components, a hybrid topological phase emerges, featuring dispersive Majorana edge modes that coexist with nearly flat Majorana edge states. Our findings therefore establish a platform for controlling and manipulating Majorana modes in unconventional superconductors with vanishing total magnetization.

Understanding the dynamic response of Ce-La alloys under extreme pressures is critical for unraveling their complex high-pressure behaviors and establishing accurate multiphase equations of states (EOSs). While existing studies focus on pressures below 20 GPa, the shock response at higher pressures remains poorly characterized. Here, we conducted front-surface-impact (FSI) shock experiments on a Ce-5 wt.% La alloy dynamically compressed to 100 GPa, enabling direct measurements of the Hugoniot curve, longitudinal and bulk sound velocities $(C_L \text{and}–C_B)$, and Grüneisen parameter $\left(\gamma \right)$. Our results revealed distinct slope changes in shock velocity $\left(u_s\right)$ and $C_B$ as functions of particle velocity $\left(u_p\right)$, accompanied by abrupt discontinuities in $C_L$ and $\gamma$. These observations, coupled with elastic-plastic to fully plastic release behavior and the merging of $C_L$ into $C_B$, provide strong evidence of shock-induced melting, allowing us to determine the melting boundary initiating at $\sim 13$ GPa and completing below 21.91 GPa. Notably, in the liquid phase, $\gamma$ exhibits an anomalous increase with density $\left(\rho \right)$, which deviates from the conventional assumption $\gamma \rho \cong {\gamma }_0{\rho }_0$. Furthermore, La additives were found to enhance sound velocities and elevate both the onset and completion pressures of melting compared to pure Ce. The experimental $P\text{−}V$ and $u_s\text{−}{u}_p$ data confirm the validity of the law of additive volumes for ideal mixtures in describing the liquid-phase response up to 100 GPa. These findings advance the understanding of multiphase properties in Ce-based alloys under dynamic compression and elucidate the regulatory role of La additives. They provide critical insights for constructing wide-range multiphase EOSs and studying phase-transition kinetics in heavy actinide surrogates.

Based on first-principles calculations and ab initio molecular-dynamics simulations, the polymerization of the unsaturated cis dinitrogen-difluoride $\left(cis\text{−}{\mathrm{N}}_2{\mathrm{F}}_2\right)$ molecular compound is investigated. The thermodynamic, dynamical, and thermal stabilities of the nitrogen fluorine (NF) system are investigated at conditions of 0–3000 K and 0–200 GPa. The $cis\text{−}{\mathrm{N}}_2{\mathrm{F}}_2$ molecule is a suitable precursor to obtain one-dimensional polymerized nitrogen-fluorine (poly-NF) chains at a pressure above 90 GPa and at a temperature around 1900 K. Importantly, these poly-NF chains can be quenched to ambient conditions, and potentially serve as a high-energy-density material. It has been established that when Al is utilized as a reducing agent, poly-NF chains exhibit a gravimetric energy density of 13.55 kJ/g, which exceeds that of cubic gauche nitrogen (cg-N, 9.70 kJ/g). This is attributable to the presence of both polymerized nitrogen and strong oxidizing F atoms.

The manipulation of the spin degree of freedom in topological electronics has provided a critical physical foundation for innovation in the information field, while phonon chirality also exhibits the potential for transmitting and storing information. In this work, we realize regulable topological chiral phonons in a monolayer hexagonal lattice by introducing an external magnetic field. The magnetic field enables the manipulation of the chirality degree of freedom and localized directional transport of phonon states, and their specific performances are determined by the competition between the breaking of inversion symmetry and time-reversal symmetry. Using the nonequilibrium Green's function method, we intuitively demonstrate the transport of topological chiral phonons. For the system with the constraint of inversion symmetry, the edge transport of chiral modes exhibits reciprocity, whereas the symmetry-broken system manifests asymmetric transport with unilateral strong localization. Our work is expected to provide pathways for information transmission and manipulation and offers potential strategies for the design of low-dissipation chiral phonon devices.

Although magnetoelectric effects in metals are usually neglected, assuming that applied electric fields are screened by free charge carriers, the skin depth, defining the penetration depth of the fields, is nonzero and for terahertz electric fields typically reaches 400 nm. Hence, if the thickness of an antiferromagnetic film is of the order of tens of nanometers, electric field induced effects cannot be neglected. Here, we theoretically study the terahertz electric field induced spin dynamics in the metallic antiferromagnet ${\mathrm{Mn}}_2\mathrm{Au}$, the spin arrangements of which allow it to exhibit a linear magnetoelectric effect. We show that the terahertz magnetoelectric torque in metallic antiferromagnets is proportional to the time derivative of the polarization induced by the terahertz electric field. Our simulations reveal that the magnetoelectric driven spin dynamics is indeed not negligible, and for a fair explanation of previously published experimental results in ${\mathrm{Mn}}_2\mathrm{Au}$ competition between terahertz magnetoelectric and Néel spin-orbit torques must be taken into account. Thus, it is shown that even in metallic antiferromagnets the terahertz magnetoelectric effect on spins can be strong and thus cannot be neglected.

Lanthanide-based single-molecule magnets (SMMs) have garnered extensive attention in recent decades for their potential applications in magnetic memory and quantum computing. In ligand field theory, the magnetic properties of a lanthanide ion may have to be characterized by up to 27 ligand field parameters. However, common experimental data such as temperature-dependent susceptibility curves measured on powder samples typically lack distinctive features. This leads to a massive over-parametrization, where multiple parameter sets can equally describe the data. In this work the issue is tackled by applying a deep learning architecture which combines a variational autoencoder (VAE) with an invertible neural network (INN). This VAE-INN architecture is shown to be capable of determining multiple ligand field parameter sets by extracting hidden parameters from the magnetic data and mapping them to the space of ligand field parameters. The approach is tested on simulated and experimental susceptibility data in magnetic models involving second-order ligand field parameters and is gradually extended to higher-order parameters until it is found limited by dimensionality issues. Compared with traditional least-squares fitting methods, the proposed approach exhibits enhanced generalization, robustness, and convergence. The present investigation of the VAE-INN architecture can be hoped to pave the way for further exploration of higher-order ligand field parameters.

Aging in a single-crystal spin glass $\left({\mathrm{Cu}}_{0.92}{\mathrm{Mn}}_{0.08}\right)$ has been measured using ac susceptibility techniques over a temperature range of $0.3–0.8T_g$. In these studies, traditional aging experiments (or “quench” aging protocols) are compared to aging curves constructed from finite-cooling-rate curves. By comparing the growth rates of spin glass order between the two types of aging curves, it is determined that quantitative comparisons between protocols that are taken by quenching and protocols using a finite cooling rate are not possible without a deeper understanding of the interplay between aging and rejuvenation. We then demonstrate that the data presented indicate that rejuvenation, rather than cumulative aging, is the cause of the discrepancies between the two growth rates.

We investigate the role of atomic distortions in nonrelativistic spin splitting in perovskite oxides with $Pbnm$ symmetry. Using ${\mathrm{LaMnO}}_3$ as a representative material, we analyze its nonrelativistic spin splitting through a combined phonon and multipolar analysis. Our study provides key insights into how structural distortions and magnetic ordering drive ferroically ordered magnetic multipoles, which, in turn, give rise to nonrelativistic spin splitting. Based on these findings, we propose three strategies for engineering nonrelativistic spin splitting: modifying the $A$-site cation size, strain engineering, and electric field control in superlattice structures. Our work establishes a framework for designing nonrelativistic spin splitting in the Brillouin zone of oxide perovskites.

In this report, a comprehensive neutron diffraction study as a function of temperature and magnetic field up to 5 T has been carried out to evaluate the complex magnetic structures of the multiferroic material ${\mathrm{BaHoFeO}}_4$. The compound is stabilized in an orthorhombic crystal structure with Pnma space group and consists of corner-sharing Fe(1)${\mathrm{O}}_5$ and Fe(2)${\mathrm{O}}_6$ polyhedral rings formed along the $b$ axis, exhibiting complex magnetic orderings. For $T<T_{N1}$, a collinear antiferromagnetic spin-density-wave (AFM-SDW) structure of ${\mathrm{Fe}}^{3+}$ moments with ${\mathbf{k}}_{\mathbf{1}}=(0,0,0.366)$ has been observed. For $T<T_{N2}$, a commensurate magnetic ordering with ${\mathbf{k}}_{\mathbf{2}}=(0.5,0,0.5)$ arises from both the ${\mathrm{Fe}}^{3+}$ and ${\mathrm{Ho}}^{3+}$ sites, forming interchain AFM and intrachain AFM correlations, respectively. Further, the magnetic structure at $T<T_{N3}$ is attributed to a multi-$\mathbf{k}$ noncoplanar noncollinear antiferromagnet with ${\mathbf{k}}_{\mathbf{2}}(0.5,0,0.5)+{\mathbf{k}}_{\mathbf{3}}(0,0,0.5)$. The analysis of magnetic-field-dependent neutron powder diffraction (NPD) data reveals a significant influence of the magnetic field on the lattice parameters and the magnetic spin structures of ${\mathrm{BaHoFeO}}_4$. A complex magnetic phase diagram in the H-T plane consisting of six ordered magnetic states has been determined. The corroboration of metamagnetic transitions to the microscopic magnetic structures at respective magnetic critical fields is established. The study demonstrates a strong coupling between lattice parameters and magnetic spin orientations, positioning ${\mathrm{BaHoFeO}}_4$ as a promising temperature- and field-induced spin-lattice-coupled magnetodielectric material.

Rare-earth-based-in-plane-ordered MAX phases ($R\text{−}i$-MAX) are a family of nano-laminated compounds with chemical formula (${\mathrm{Mo}}_{2/3}{R}_{1/3}{)}_2\text{AlC}$ that have attracted interest as potential precursors for magnetic two-dimensional (2D) derivatives. Experimental investigations of the magnetic properties of these materials have revealed complicated magnetic phase diagrams with multiple magnetic phase transitions as a function of temperature and external field, commensurate and incommensurate magnetic ordering, as well as fluctuations of the magnetic moments when rare-earths heavier than Gd are introduced. In this work, the magnetic exchange interactions of $R\text{−}i$-MAX phases, where $R$ = Nd, Sm, Gd, Tb, Dy, Ho, and Er are calculated using density functional theory and are measured experimentally using magnetic diffuse neutron scattering measurements on powder samples with $R$ =Tb and Er. Good quantitative agreement is found between the measured and calculated exchange interactions, as well as between the observed and calculated relative magnetic ordering temperatures. The strongest interaction is found to be for rare-earths separated by the Al layer, with much weaker interactions in the carbide layer. These results may have significant implications on the existence of magnetism in the two-dimensional derivatives of the MAX phases. This study is an initial step in developing a computational framework for the prediction and optimization of potential 2D magnets in the $R\text{−}i$-MAX family of compounds.

Most of the superconductors with nontrivial band topology discovered so far are constrained to materials with low superconducting transition temperatures $\left(T_{\mathrm{c}}\right)$ and narrow topological energy gaps. Here we use first-principles calculations to demonstrate that ${\mathrm{KTeO}}_3$ can be converted into high-$T_{\mathrm{c}}$ superconductors with concomitant large topological energy gaps via effective suppression of the multivalency of Te. We first show that the inherent multivalent nature of Te in pristine ${\mathrm{KTeO}}_3$, accompanied by too strong electron-phonon coupling, leads to a dominant charge density wave (CDW) instability. Next, we find that when the Te multivalency is suppressed by proper gating or partially substituting K with Ba at moderate pressure, the electron-phonon coupling is significantly weakened, and the CDW instability yields to a dominant superconducting order with a maximum $T_{\mathrm{c}}$ of ∼60 K right at the CDW-to-superconductivity transition. Furthermore, the superconducting systems exhibit nontrivial band topology with unusually wide energy gaps of ∼0.8 eV, thereby serving as appealing platforms for realizing topological superconductivity with exceptional robustness and tunability.